In mathematics, a Poisson superalgebra-graded that is equipped with a second bilinear map,

1. .

the bracket satisfies:

• .

• .

• .

This is one of two possible ways of "super"izing the Poisson algebra. This gives the classical dynamics of fermion fields and classical spin-1/2 particles. The other way is to define an antibracket algebra or Gerstenhaber algebra, used in the BRST and Batalin-Vilkovisky formalism. The difference between these two is in the grading of the Lie bracket. In the Poisson superalgebra, the grading of the bracket is zero:

whereas in the Gerstenhaber algebra, the bracket decreases the grading by one:

Examples

• is any associative into a Poisson superalgebra.

• .

See also

• Poisson supermanifold

References